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1 | /* |
2 | * rational fractions |
3 | * |
4 | * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <os@emlix.com> |
5 | * |
6 | * helper functions when coping with rational numbers |
7 | */ |
8 | |
9 | #include <linux/rational.h> |
10 | |
11 | /* |
12 | * calculate best rational approximation for a given fraction |
13 | * taking into account restricted register size, e.g. to find |
14 | * appropriate values for a pll with 5 bit denominator and |
15 | * 8 bit numerator register fields, trying to set up with a |
16 | * frequency ratio of 3.1415, one would say: |
17 | * |
18 | * rational_best_approximation(31415, 10000, |
19 | * (1 << 8) - 1, (1 << 5) - 1, &n, &d); |
20 | * |
21 | * you may look at given_numerator as a fixed point number, |
22 | * with the fractional part size described in given_denominator. |
23 | * |
24 | * for theoretical background, see: |
25 | * http://en.wikipedia.org/wiki/Continued_fraction |
26 | */ |
27 | |
28 | void rational_best_approximation( |
29 | unsigned long given_numerator, unsigned long given_denominator, |
30 | unsigned long max_numerator, unsigned long max_denominator, |
31 | unsigned long *best_numerator, unsigned long *best_denominator) |
32 | { |
33 | unsigned long n, d, n0, d0, n1, d1; |
34 | n = given_numerator; |
35 | d = given_denominator; |
36 | n0 = d1 = 0; |
37 | n1 = d0 = 1; |
38 | for (;;) { |
39 | unsigned long t, a; |
40 | if ((n1 > max_numerator) || (d1 > max_denominator)) { |
41 | n1 = n0; |
42 | d1 = d0; |
43 | break; |
44 | } |
45 | if (d == 0) |
46 | break; |
47 | t = d; |
48 | a = n / d; |
49 | d = n % d; |
50 | n = t; |
51 | t = n0 + a * n1; |
52 | n0 = n1; |
53 | n1 = t; |
54 | t = d0 + a * d1; |
55 | d0 = d1; |
56 | d1 = t; |
57 | } |
58 | *best_numerator = n1; |
59 | *best_denominator = d1; |
60 | } |
61 | |
62 | EXPORT_SYMBOL(rational_best_approximation); |
63 |
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